Promoting multiexciton interactions in singlet fission and triplet fusion upconversion dendrimers

Singlet fission and triplet-triplet annihilation upconversion are two multiexciton processes intimately related to the dynamic interaction between one high-lying energy singlet and two low-lying energy triplet excitons. Here, we introduce a series of dendritic macromolecules that serve as platform to study the effect of interchromophore interactions on the dynamics of multiexciton generation and decay as a function of dendrimer generation. The dendrimers (generations 1–4) consist of trimethylolpropane core and 2,2-bis(methylol)propionic acid (bis-MPA) dendrons that provide exponential growth of the branches, leading to a corona decorated with pentacenes for SF or anthracenes for TTA-UC. The findings reveal a trend where a few highly ordered sites emerge as the dendrimer generation grows, dominating the multiexciton dynamics, as deduced from optical spectra, and transient absorption spectroscopy. While the dendritic structures enhance TTA-UC at low annihilator concentrations in the largest dendrimers, the paired chromophore interactions induce a broadened and red-shifted excimer emission. In SF dendrimers of higher generations, the triplet dynamics become increasingly dominated by pairwise sites exhibiting strong coupling (Type II), which can be readily distinguished from sites with weaker coupling (Type I) by their spectral dynamics and decay kinetics.

There is a noticeable shift in the UCPL spectra with increasing dendrimer size ( Figure 2c, and normalized PL in Supplementary Fig. 3). The UCPL spectrum of [G1]-A6 most similarly resembles that of TIPS-An-BE but with increased dendrimer generation there is a decrease in UCPL at the highest energy peak (462 nm) and increase UCPL at lower energy (500-600 nm). This is indicative of excimer formation, typically observed in environments which promote aggregation, such as concentrated solutions or in poorly solubilizing solvents. These results support that larger dendrimers increase the local annihilator concentration, even into a regime where TTA-UC becomes less efficient.
Increasing the concentration of dendrimer in solution from 1 to 5, 10, 25, and 50 μM, with the concentration of PdTPTBP constant at 50 μM, results in an increasing intensity in the UCPL.
Integrated UCPL intensity is summarized in Table 2. At low effective annihilator concentrations, dendrimers produce a higher UCPL intensity than TIPS-An-BE monomer, regardless of dendrimer  We measure a triplet transfer yield of 40% at ~50 μM annihilator concentration, corresponding to ~ 5% probability of transferring two triplet excitons to the same dendrimer. This value agrees well with UCPL characterization, which exhibits a low but measurable yield.

C. Numerical Simulations
We modeled the dendrimer using a bead-and-spring model held together by harmonic springs of the form Us= /2 (r-r0) 2 with spring constant  =300 kBT/   Here  is the diameter of the monomers, kB is the Boltzmann constant, and the equilibrium distance r0= To enforce excluded volume interactions between the monomers, we use a MIE potential of the form Ue= 4 [ (/r) 24 − (/r) 12 ], cut of at r=2 1/12 , with  = kBT.
The outer pentacene molecules are modeled as rectangular frames formed by a matrix of 3x spherical particles also of diameter  (here  is the longitudinal length of the pentacene molecule which we vary) arranged in a planar square lattice as shown in Supplementary Fig. 8a. The shape of the pentacene is held together by the spring potential Us and a bending potential of the form Ub=kb(−)  between the particles along the columns and along the rows of the rectangle. The bending rigidity is set to kb= 250 kBT. The particles on the sides of the rectangle are there to merely enforce the planar shape of the molecule and interact with any other monomer in the dendrimer with the same excluded volume potential Ue. The monomers in the middle mediate the pentacenepentacene attractive interactions which are set-up using the same MIE potential defined above to impose excluded volume interactions, but now with a cut-off that extends up to r=1.5 (so that an attractive interaction emerges on top of the excluded volume) and  in this case is set in the range of (3.5 − ) kBT (the strength of the attraction).
The molecular dynamics simulations are carried out using the numerical package LAMMPS 1 and the equations of motion follows a standard Langevin dynamics Here g is the friction coefficient, which is set to 1, h is the Gaussian distributed and uncorrelated thermal noise, and F are the forces arising from the derivative of the potentials discussed above.
In our simulations  and kBT are used as the units of length and energy scales of the system, while

b. Target analysis of fs TA and global analysis of ns TA
To capture the full multiscale exciton dynamics of the SF dendrimers, we have constructed a model that partitions the spin conversion process into two distinct branches to account for the differing morphology of chromophores within a single dendrimer generation. For the fs TA data, our model starts with a common singlet state for Type I and Type II that then branches into two distinct ensembles. For simplicity, the branching ratio was set to 0.4 Type I and 0.6 Type II based on the approximate excited state population remaining following the initial fast (~ 1 ns) population loss ( Figure 4e). Within the Type I branch, a portion of the initial singlet exciton population decays via a fast singlet fission step ( , ) into a second species that represents a mixture of Type I specific singlet excitons and Type I triplet pairs. This is followed by a slower SF step ( , ) that fully converts the excited state population to triplet pairs. The triplet pairs decay in the usual via excitonexciton annihilation ( ) which leaves behind a residual population of free triplets that decays to the ground state ( 1 ). The overall process can be summarized as:

A. Synthesis of PhBr Dendrimers
Adapted from a related literature procedure. 2 To a suspension of CDI (10 equiv. for G1/20 equiv. for G2/36 equiv. for G3/54 equiv. for G4) in EtOAc at 50℃ was added 4-bromobenzoic acid (10 equiv. for G1/20 equiv. for G2/36 equiv. for G3/54 equiv. for G3). After stirring for 1 h at 50℃, CsF (1.2 equiv. for G1/2.4 equiv. for G2/4.8 equiv. for G3/9.6 equiv. for G4) and the hydroxylterminated dendrimer (1 equiv.) were added. The reaction was stirred at 50°C overnight. The reaction was cooled to r.t. and quenched by stirring with water for 1 h. After quenching, the mixture was diluted with EtOAc, washed with NaHCO3, dried over Na2SO4, and concentrated down. The crude was dissolved in a minimal amount of EtOAc and purified by MeOH precipitation. A representative reaction is shown in Supplementary Fig. 27.  Supplementary Fig. 27

C. Synthesis of TIPS-Anthracene Dendrimers
To a vial was added PhBr dendrimer ([Gn]-PhBrx), TIPS-anthracene-2-boronic acid pinacol ester (10 equiv. for G1/16 equiv. for G2/30 equiv. for G3/54 equiv. for G4), potassium carbonate, and Pd(dppf)Cl2·DCM under inert atmosphere. Dry, degassed THF and degassed water were added, and the reaction was allowed to stir at 75°C for 24 h. After the mixture was cooled to room temperature, it was dried with Na2SO4 and concentrated under reduced pressure. Crude solid was purified by silica gel column chromatography with 0-100% DCM/hexanes eluent, followed by precipitation into methanol at 0°C to afford desired product as yellow solid.